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Abstract
The modification of the vorticity spectrum associated with the use of finite differences instead of derivatives is considered for an isotropic turbulence field. The results permit a rough estimate of the dependence of the magnitude of vorticity on the grid spacing.
Abstract
The modification of the vorticity spectrum associated with the use of finite differences instead of derivatives is considered for an isotropic turbulence field. The results permit a rough estimate of the dependence of the magnitude of vorticity on the grid spacing.
Abstract
Wave solutions of the non-linear quasi-geostrophic equations for the so-called “2½-dimensional model” without friction are derived. The solutions describe wave motions which propagate at different speeds in each layer. The amplitudes of the disturbances, are either changing periodically with time (stable waves) or increasing exponentially (unstable waves). The critical value of wavelength, at which waves maintain a constant amplitude, is expressed as a function of thermal stability and of vertical wind shear in the basic current.
It is also found that, while the inclination of trough lines to the vertical increases monotonically with time in stable waves, it varies very slowly in the unstable waves and tends to approach a certain limiting value.
Abstract
Wave solutions of the non-linear quasi-geostrophic equations for the so-called “2½-dimensional model” without friction are derived. The solutions describe wave motions which propagate at different speeds in each layer. The amplitudes of the disturbances, are either changing periodically with time (stable waves) or increasing exponentially (unstable waves). The critical value of wavelength, at which waves maintain a constant amplitude, is expressed as a function of thermal stability and of vertical wind shear in the basic current.
It is also found that, while the inclination of trough lines to the vertical increases monotonically with time in stable waves, it varies very slowly in the unstable waves and tends to approach a certain limiting value.
Abstract
The correlation functions obtained from truncated samples are expressed in terms of the sampling length and the correlation functions of the basic stationary random variables. The application of the results to diffusion phenomena in a turbulent flow is discussed. The investigation brings out the influence of confining oneself to finite observation intervals on the average rate of dispersion of particles from a point source. It is also shown that the turbulent level is of importance in determining the relationship between the Eulerian and Lagrangian time intervals of observation.
Abstract
The correlation functions obtained from truncated samples are expressed in terms of the sampling length and the correlation functions of the basic stationary random variables. The application of the results to diffusion phenomena in a turbulent flow is discussed. The investigation brings out the influence of confining oneself to finite observation intervals on the average rate of dispersion of particles from a point source. It is also shown that the turbulent level is of importance in determining the relationship between the Eulerian and Lagrangian time intervals of observation.
Abstract
The study of the life history of the 8 June 1966 squall line by Ogura and Chen (1977) indicates that a well-defined narrow hand of horizontal convergence was present at low levels prior to the appearance of first radar echoes. A two-dimensional model for the dry planetary boundary layer is developed and applied to this case in order to test the hypothesis that the prestorm convergence is produced by boundary-layer processes in association with a strong horizontal temperature gradient. The level 3 turbulence closure approximation by Mellor and Yamada (1974) is incorporated into the model as well as the similarity hypothesis of Businger et al. (1971) for the lowest constant flux layer. The basic driving mechanism is the diurnal variation of the temperature contrast across the observed dry line. Air on the northwest side was warm, while on the southeast side it was cool. The temperature contrast was introduced into the model as a lower boundary condition for the potential temperature.
The model is integrated, starting from the early morning conditions through the late afternoon. The results indicate the development of ascending-descending motions as soon as a horizontal temperature gradient is established. In time, the mixed layer also develops and its depth increases. AS expected, it increases faster on the warm side than on the cool side. The intensity of the upward motion increases at a rate larger than that of the downward motion and the center of the ascending motion remains at a certain level (∼800 mb). The center of the downward motion moves up in time. Thus, the upward motion is concentrated in the mixed layer at the location of the sharp gradient in the inversion. The major observed features in the velocity and temperature fields in the prestorm situation are well simulated by the model. Further, the result of a sensitivity test for a different initial wind field indicates that the location and intensity of the. resulting ascending motion is rather sensitive to the initial wind field. It is concluded that, if the synoptic-scale low-level wind blows in the right direction (off shore in sea-breeze terminology), a low-level horizontal temperature gradient of the magnitude observed in the 8 June 1966 squall line case is capable of generating upward motion with sufficient intensity to release the potential instability.
Abstract
The study of the life history of the 8 June 1966 squall line by Ogura and Chen (1977) indicates that a well-defined narrow hand of horizontal convergence was present at low levels prior to the appearance of first radar echoes. A two-dimensional model for the dry planetary boundary layer is developed and applied to this case in order to test the hypothesis that the prestorm convergence is produced by boundary-layer processes in association with a strong horizontal temperature gradient. The level 3 turbulence closure approximation by Mellor and Yamada (1974) is incorporated into the model as well as the similarity hypothesis of Businger et al. (1971) for the lowest constant flux layer. The basic driving mechanism is the diurnal variation of the temperature contrast across the observed dry line. Air on the northwest side was warm, while on the southeast side it was cool. The temperature contrast was introduced into the model as a lower boundary condition for the potential temperature.
The model is integrated, starting from the early morning conditions through the late afternoon. The results indicate the development of ascending-descending motions as soon as a horizontal temperature gradient is established. In time, the mixed layer also develops and its depth increases. AS expected, it increases faster on the warm side than on the cool side. The intensity of the upward motion increases at a rate larger than that of the downward motion and the center of the ascending motion remains at a certain level (∼800 mb). The center of the downward motion moves up in time. Thus, the upward motion is concentrated in the mixed layer at the location of the sharp gradient in the inversion. The major observed features in the velocity and temperature fields in the prestorm situation are well simulated by the model. Further, the result of a sensitivity test for a different initial wind field indicates that the location and intensity of the. resulting ascending motion is rather sensitive to the initial wind field. It is concluded that, if the synoptic-scale low-level wind blows in the right direction (off shore in sea-breeze terminology), a low-level horizontal temperature gradient of the magnitude observed in the 8 June 1966 squall line case is capable of generating upward motion with sufficient intensity to release the potential instability.
Abstract
A system of shallow-fluid equations on the rotating earth is integrated numerically as an initial and boundary value problem for air flow across a mountain barrier. The fluid is confined in a channel bounded by two parallel walls at 30N and 70S. The (idealized) Andes Mountains considered here are 4.75 km high and about 200 km wide on their western slope. A variable map factor in the east-west direction is applied so that the model permits increased resolution near steep topographic features. The scheme is found to be quite stable. The result is compared with a case where the mountains are smoothed and an equidistant grid is applied. Brief descriptions of dissimilarity between westerly and easterly flows across the barrier and the two-dimensional cascade process are also given.
Abstract
A system of shallow-fluid equations on the rotating earth is integrated numerically as an initial and boundary value problem for air flow across a mountain barrier. The fluid is confined in a channel bounded by two parallel walls at 30N and 70S. The (idealized) Andes Mountains considered here are 4.75 km high and about 200 km wide on their western slope. A variable map factor in the east-west direction is applied so that the model permits increased resolution near steep topographic features. The scheme is found to be quite stable. The result is compared with a case where the mountains are smoothed and an equidistant grid is applied. Brief descriptions of dissimilarity between westerly and easterly flows across the barrier and the two-dimensional cascade process are also given.
Abstract
The genesis and development of an intermediate-scale cyclone in middle latitudes was simulated numerically and its three-dimensional structure analysed.
A six-level moist primitive equation model was run for a channel flow with an initial weak baroclinicity. The motion was initiated in the flow by introducing wave motion with wavelength of 6000 km. As the initial disturbance was intensified, an extended front developed and, after several days in real time, an intermediate-scale disturbance was formed on the extended front. The analysis indicates that this secondary cyclone has a longitudinal wavelength of about 1500 km and a latitudinal half-wavelength of about 600 km. The depression is observed most strongly below 700 mb with a vertical or slightly eastward tilted trough axis. A sharp concentration of isotherms is situated in the northern part of the cyclone. In the lower troposphere, the warm air is observed on the cast side of the low center and the cold air on the west side. This thermal contrast is reversed in the middle troposphere. A remarkable accumulation of water vapor assumes a pear-like shape over the depression area. The thermal structure of the simulated depression was compared with the observed data and some agreement was noted. The effect of the water vapor was also examined in the evolution of the simulated intermediate-scale cyclone.
Abstract
The genesis and development of an intermediate-scale cyclone in middle latitudes was simulated numerically and its three-dimensional structure analysed.
A six-level moist primitive equation model was run for a channel flow with an initial weak baroclinicity. The motion was initiated in the flow by introducing wave motion with wavelength of 6000 km. As the initial disturbance was intensified, an extended front developed and, after several days in real time, an intermediate-scale disturbance was formed on the extended front. The analysis indicates that this secondary cyclone has a longitudinal wavelength of about 1500 km and a latitudinal half-wavelength of about 600 km. The depression is observed most strongly below 700 mb with a vertical or slightly eastward tilted trough axis. A sharp concentration of isotherms is situated in the northern part of the cyclone. In the lower troposphere, the warm air is observed on the cast side of the low center and the cold air on the west side. This thermal contrast is reversed in the middle troposphere. A remarkable accumulation of water vapor assumes a pear-like shape over the depression area. The thermal structure of the simulated depression was compared with the observed data and some agreement was noted. The effect of the water vapor was also examined in the evolution of the simulated intermediate-scale cyclone.
Abstract
A one-and-a-half-dimensional, time-dependent cloud model proposed by the authors is extended to investigate warm-rain formation. A total of 61 mass categories, corresponding to radii from 4 μm to 4 mm, are used to determine the drop distribution. The distribution of hydrometeors evolves with time as a result of condensation, evaporation, stochastic coalescence, sedimentation, and drop breakup. The formation of liquid drops around condensation nuclei is parameterized to take a prescribed drop size distribution, though the number concentration of nuclei is predicted. Three different types of the prescribed initial size distribution of drops are considered to test their control of the subsequent hydrometeor distribution.
Convection is initiated in a conditionally unstable atmosphere which represents tradewind conditions, and long time integrations of the model are performed to cover the entire life cycle of a simulated cumulus cloud. In a typical case, the maximal updraft resulting from the calculation is 4.7 m sec−1 and the rate of rainfall reaches its peak of 27 mm hr−1 10 min after rainfall has started at the ground. The rain continues for 25 min and the total amount of rainfall is 4.5 min. Some aspects of maritime warm cumulus and rainfall seem to he simulated, such as the sudden onset of large-drop rain in convective showers. The predicted size distributions for raindrops are compared with the Marshall-Palmer distribution with fairly good agreement. It is also found that the broad initial size distribution generates the onset and end of precipitation earlier than the narrow size distribution.
Abstract
A one-and-a-half-dimensional, time-dependent cloud model proposed by the authors is extended to investigate warm-rain formation. A total of 61 mass categories, corresponding to radii from 4 μm to 4 mm, are used to determine the drop distribution. The distribution of hydrometeors evolves with time as a result of condensation, evaporation, stochastic coalescence, sedimentation, and drop breakup. The formation of liquid drops around condensation nuclei is parameterized to take a prescribed drop size distribution, though the number concentration of nuclei is predicted. Three different types of the prescribed initial size distribution of drops are considered to test their control of the subsequent hydrometeor distribution.
Convection is initiated in a conditionally unstable atmosphere which represents tradewind conditions, and long time integrations of the model are performed to cover the entire life cycle of a simulated cumulus cloud. In a typical case, the maximal updraft resulting from the calculation is 4.7 m sec−1 and the rate of rainfall reaches its peak of 27 mm hr−1 10 min after rainfall has started at the ground. The rain continues for 25 min and the total amount of rainfall is 4.5 min. Some aspects of maritime warm cumulus and rainfall seem to he simulated, such as the sudden onset of large-drop rain in convective showers. The predicted size distributions for raindrops are compared with the Marshall-Palmer distribution with fairly good agreement. It is also found that the broad initial size distribution generates the onset and end of precipitation earlier than the narrow size distribution.
Abstract
The two-dimensional slab-symmetric numerical cloud model used by Soong and Ogura (1973) for studying the evolution of an isolated cumulus cloud is extended to investigate the statistical properties of cumulus clouds which would be generated under a given large-scale forcing composed of the horizontal advection of temperature and water vapor mixing ratio, vertical velocity, sea surface temperature and radiative cooling. Random disturbances of small amplitude are introduced into the model at low levels to provide random motion for cloud formation.
The model is applied to a case of suppressed weather conditions during BOMEX for the period 22–23 June 1969 when a nearly steady state prevailed. The composited temperature and mixing ratio profiles of these two days are used as initial conditions and the time-independent large-scale forcing terms estimated from the observations are applied to the model. The result of numerical integration shows that a number of small clouds start developing after 1 h. Some of them decay quickly, but some of them develop and reach the tradewind inversion. After a few hours of simulation, the vertical profiles of the horizontally averaged temperature and moisture are found to deviate only slightly from the observed profiles, indicating that the large-scale effect and the feedback effects of clouds on temperature and mixing ratio reach an equilibrium state. The three major components of the cloud feedback effect, i.e., condensation, evaporation and vertical fluxes associated with the clouds, are determined from the model output. The vertical profiles of vertical heat and moisture fluxes in the subcloud layer in the model are found to be in general agreement with the observations.
Sensitivity tests of the model are made for different magnitudes of the large-scale vertical velocity. The most striking result is that the temperature and humidity in the cloud layer below the inversion do not change significantly in spite of a relatively large variation in height and intensity of the trade-wind inversion. This may indicate that cumulus clouds respond quickly to the large-scale forcing and adjust their own transport properties to maintain the observed large-scale thermodynamic fields whose variation has a much longer time scale. Sensitivity tests on varying sea surface temperature indicate that a ±1°C change in the sea surface temperature does not change the height of the inversion significantly during a 6 h simulation period. Another simulation shows that a tradewind inversion can develop rapidly from an initial sounding without an inversion if the large-scale downward motion is fairly large.
Abstract
The two-dimensional slab-symmetric numerical cloud model used by Soong and Ogura (1973) for studying the evolution of an isolated cumulus cloud is extended to investigate the statistical properties of cumulus clouds which would be generated under a given large-scale forcing composed of the horizontal advection of temperature and water vapor mixing ratio, vertical velocity, sea surface temperature and radiative cooling. Random disturbances of small amplitude are introduced into the model at low levels to provide random motion for cloud formation.
The model is applied to a case of suppressed weather conditions during BOMEX for the period 22–23 June 1969 when a nearly steady state prevailed. The composited temperature and mixing ratio profiles of these two days are used as initial conditions and the time-independent large-scale forcing terms estimated from the observations are applied to the model. The result of numerical integration shows that a number of small clouds start developing after 1 h. Some of them decay quickly, but some of them develop and reach the tradewind inversion. After a few hours of simulation, the vertical profiles of the horizontally averaged temperature and moisture are found to deviate only slightly from the observed profiles, indicating that the large-scale effect and the feedback effects of clouds on temperature and mixing ratio reach an equilibrium state. The three major components of the cloud feedback effect, i.e., condensation, evaporation and vertical fluxes associated with the clouds, are determined from the model output. The vertical profiles of vertical heat and moisture fluxes in the subcloud layer in the model are found to be in general agreement with the observations.
Sensitivity tests of the model are made for different magnitudes of the large-scale vertical velocity. The most striking result is that the temperature and humidity in the cloud layer below the inversion do not change significantly in spite of a relatively large variation in height and intensity of the trade-wind inversion. This may indicate that cumulus clouds respond quickly to the large-scale forcing and adjust their own transport properties to maintain the observed large-scale thermodynamic fields whose variation has a much longer time scale. Sensitivity tests on varying sea surface temperature indicate that a ±1°C change in the sea surface temperature does not change the height of the inversion significantly during a 6 h simulation period. Another simulation shows that a tradewind inversion can develop rapidly from an initial sounding without an inversion if the large-scale downward motion is fairly large.
Abstract
A case of squall line generation in the National Severe Storms Laboratory (NSSL) network has been examined with the intention of capturing synoptic-scale influences. A telescopic analysis approach was used whereby observations from both synoptic and mesoscale networks were combined.
The squall line formed in the warm air behind the surface position of the cold front. Large-scale circulation was responsible for creating a shallow layer (∼1-km thick) of convectively unstable air immediately above this front. Horizontal gradient of low-level moisture, pronounced low-level wind shear, and surface convergence were the large-scale factors that combined to produce the unstable region.
Mesoscale analysis showed that vertical velocity in the low levels exhibited a persistent small-scale variation prior to convective activity. The horizontal variation in vertical velocity was ultimately responsible for creating a favored position within the mesonetwork.
Conservation of potential temperature and specific humidity is examined as well as the relative importance of horizontal and vertical advection.
Abstract
A case of squall line generation in the National Severe Storms Laboratory (NSSL) network has been examined with the intention of capturing synoptic-scale influences. A telescopic analysis approach was used whereby observations from both synoptic and mesoscale networks were combined.
The squall line formed in the warm air behind the surface position of the cold front. Large-scale circulation was responsible for creating a shallow layer (∼1-km thick) of convectively unstable air immediately above this front. Horizontal gradient of low-level moisture, pronounced low-level wind shear, and surface convergence were the large-scale factors that combined to produce the unstable region.
Mesoscale analysis showed that vertical velocity in the low levels exhibited a persistent small-scale variation prior to convective activity. The horizontal variation in vertical velocity was ultimately responsible for creating a favored position within the mesonetwork.
Conservation of potential temperature and specific humidity is examined as well as the relative importance of horizontal and vertical advection.
Abstract
Surface and upper air data gathered from a dense network of ship observations during the GARP Atlantic Tropical Experiment (GATE) were analyzed to correlate the upward motion with organized cloud convection. Two periods were. selected for analysis, 11–12 August and 3–6 September, 1974. The first period covers a case in which a spectacular development of an ITCZ rainband was observed. During the second period six cloud clusters were identified from radar and satellite photographs which either formed or intensified. within the data area under consideration.
The key variable in the analysis was the horizontal velocity divergence which was calculated using an objective analysis scheme. The, vertical velocity was then computed kinematically. The analysis results reveal good correlation between the vertical velocity fields and the development of organized convective systems. In all cases considered, the low-level convergence and, consequently, upward motion was present or enhanced prior to the development of organized convective systems. In some cases weak descending motion was observed in the upper troposphere. A low-level inversion was absent in the area of subsequent convective development in contrast to other areas having no organized convective activity. As organized convective systems developed, the upward motion intensified and extended up to the tropopause. The horizontal distributions of precipitation rates estimated from the moisture budget were compared to those calculated by Hudlow (1977) from radar measurements with fair agreement. A comparison was also made between the point value of the vertical velocity calculated by the analysis scheme and the vertical velocity averaged over the outer ship army or A/B-scale area.
Abstract
Surface and upper air data gathered from a dense network of ship observations during the GARP Atlantic Tropical Experiment (GATE) were analyzed to correlate the upward motion with organized cloud convection. Two periods were. selected for analysis, 11–12 August and 3–6 September, 1974. The first period covers a case in which a spectacular development of an ITCZ rainband was observed. During the second period six cloud clusters were identified from radar and satellite photographs which either formed or intensified. within the data area under consideration.
The key variable in the analysis was the horizontal velocity divergence which was calculated using an objective analysis scheme. The, vertical velocity was then computed kinematically. The analysis results reveal good correlation between the vertical velocity fields and the development of organized convective systems. In all cases considered, the low-level convergence and, consequently, upward motion was present or enhanced prior to the development of organized convective systems. In some cases weak descending motion was observed in the upper troposphere. A low-level inversion was absent in the area of subsequent convective development in contrast to other areas having no organized convective activity. As organized convective systems developed, the upward motion intensified and extended up to the tropopause. The horizontal distributions of precipitation rates estimated from the moisture budget were compared to those calculated by Hudlow (1977) from radar measurements with fair agreement. A comparison was also made between the point value of the vertical velocity calculated by the analysis scheme and the vertical velocity averaged over the outer ship army or A/B-scale area.
